def at( x, mean = 0.0, standardDeviation = 1.0) :
'''
See http://mathworld.wolfram.com/NormalDistribution.html
1 -(x-mean)^2 / (2*stdDev^2)
P(x) = ------------------- * e
stdDev * sqrt(2*pi)
'''
multiplier = 1.0/(standardDeviation*sqrt(2.0*PI))
expPart = exp((-1.0*square(x - mean))/(2.0*square(standardDeviation)))
result = multiplier*expPart;
return result
def at(x, mean=0.0, standardDeviation=1.0):
'''
See http://mathworld.wolfram.com/NormalDistribution.html
1 -(x-mean)^2 / (2*stdDev^2)
P(x) = ------------------- * e
stdDev * sqrt(2*pi)
'''
multiplier = 1.0 / (standardDeviation * sqrt(2.0 * PI))
expPart = exp(
(-1.0 * square(x - mean)) / (2.0 * square(standardDeviation)))
result = multiplier * expPart
return result
def inverseErrorFunctionCumulativeTo( p) :
''' From page 265 of numerical recipes'''
if (p >= 2.0) :
return -100
if (p <= 0.0) :
return 100
if p < 1.0 :
pp = p
else :
pp = 2 - p
t = sqrt(-2*log(pp/2.0)); # Initial guess
x = -0.70711*((2.30753 + t*0.27061)/(1.0 + t*(0.99229 + t*0.04481)) - t)
for j in range(2) :
err = GaussianDistribution.errorFunctionCumulativeTo(x) - pp
x = x + (err/(1.12837916709551257*exp(-square(x)) - x*err)) # // Halley
if p < 1.0 :
return x
else :
return -x
def inverseErrorFunctionCumulativeTo(p):
''' From page 265 of numerical recipes'''
if (p >= 2.0):
return -100
if (p <= 0.0):
return 100
if p < 1.0:
pp = p
else:
pp = 2 - p
t = sqrt(-2 * log(pp / 2.0))
# Initial guess
x = -0.70711 * ((2.30753 + t * 0.27061) /
(1.0 + t * (0.99229 + t * 0.04481)) - t)
for j in range(2):
err = GaussianDistribution.errorFunctionCumulativeTo(x) - pp
x = x + (err / (1.12837916709551257 * exp(-square(x)) - x * err)
) # // Halley
if p < 1.0:
return x
else:
return -x
def logProductNormalization(left, right) :
if ((left._precision == 0) or (right._precision == 0)) :
return 0
varianceSum = left._variance + right._variance
meanDifference = left._mean - right._mean
logSqrt2Pi = log(sqrt(2*PI));
return -logSqrt2Pi - (log(varianceSum)/2.0) - (square(meanDifference)/(2.0*varianceSum))
def logProductNormalization(left, right):
if ((left._precision == 0) or (right._precision == 0)):
return 0
varianceSum = left._variance + right._variance
meanDifference = left._mean - right._mean
logSqrt2Pi = log(sqrt(2 * PI))
return -logSqrt2Pi - (log(varianceSum) /
2.0) - (square(meanDifference) /
(2.0 * varianceSum))
def logRatioNormalization(numerator, denominator):
if ((numerator._precision == 0) or (denominator._precision == 0)):
return 0
varianceDifference = denominator._variance - numerator._variance
meanDifference = numerator._mean - denominator._mean
logSqrt2Pi = log(sqrt(2 * PI))
return log(denominator._variance) + logSqrt2Pi - log(
varianceDifference) / 2.0 + square(meanDifference) / (
2 * varianceDifference)
def __init__(self, mean=0.0, standardDeviation=1.0):
self._mean = mean
self._standardDeviation = standardDeviation
#precision and precisionMean are used because they make multiplying and dividing simpler
#(the the accompanying math paper for more details)
self._variance = square(standardDeviation)
self._precision = None
self._precisionMean = None
if self._variance != 0.0:
self._precision = 1 / self._variance
self._precisionMean = self._precision * self._mean
else:
self._precision = INF
if self._mean == 0.0:
self._precisionMean = 0.0
else:
self._precisionMean = INF
def __init__(self, mean = 0.0, standardDeviation = 1.0):
self._mean = mean
self._standardDeviation = standardDeviation
#precision and precisionMean are used because they make multiplying and dividing simpler
#(the the accompanying math paper for more details)
self._variance = square(standardDeviation)
self._precision = None
self._precisionMean = None
if self._variance != 0.0 :
self._precision = 1/self._variance
self._precisionMean = self._precision * self._mean
else :
self._precision = INF
if self._mean == 0.0 :
self._precisionMean = 0.0
else :
self._precisionMean = INF
def logRatioNormalization(numerator, denominator) :
if ((numerator._precision == 0) or (denominator._precision == 0)) :
return 0;
varianceDifference = denominator._variance - numerator._variance
meanDifference = numerator._mean - denominator._mean
logSqrt2Pi = log(sqrt(2*PI));
return log(denominator._variance) + logSqrt2Pi - log(varianceDifference)/2.0 + square(meanDifference)/(2*varianceDifference)